Thaw catfish fillets in the refrigerator. Skip this step if the catfish is fresh. Pour oil into a dutch oven or fryer. The oil should be two inches deep. Bring to a boil. It should be approximately 325 degrees. Combine pepper, salt and cornmeal in a bowl large enough for dredging catfish fillets. Pour buttermilk in a separate bowl. Dip catfish into buttermilk, making certain each side is covered. Press catfish into seasoned cornmeal mixture, then flip and coat the second side. Place catfish on a plate. Repeat dredging process with the remaining catfish fillets. Lower a breaded catfish fillet into hot oil with tongs. Cook each fillet for about 8 minutes, or until the catfish floats to the top and features a golden hue. Serve immediately.